The effects of magnetic fields on single particles or excitations in two-dimensional lattices are well known from Hofstadter's approach [1]}. The density of states for two particles for various interaction strengths had also been computed before [2]}. In optical lattices, the external magnetic fields can be synthesized with periodic modulation of the lattice potentials [3]}, [4]}, [5]}. This article specifically looks at the density of bound pairs for both zero and non-zero magnetic fields at different interaction strengths. In the context of condensed matter, the effective fields can also be realized through doping with isotropic magnetic impurities.
